Question
In: Statistics and Probability
compute the 90%, 95%, and 99% confidence interval for N=282 Mean= 2.36 SD= 1.19 explain the...
compute the 90%, 95%, and 99% confidence interval for N=282 Mean=
2.36 SD= 1.19
explain the effect of confidence interval on the width of the
interval
Solutions
Expert Solution
a) Sample size = n = 282
Sample mean = 
= 2.36
Standard deviation = s = 1.19
We have to construct 90% confidence interval.
Formula is
Here E is a margin of error.
Degrees of freedom = n - 1 = 282 - 1 = 281
Level of significance = 0.10
tc = 1.650 ( Using t table)
So confidence interval is ( 2.36 - 0.1169 , 2.36 + 0.1169) = > ( 2.2431 , 2.4769)
-------------------------------------------------------------------------------------------------------------------
b) Sample size = n = 282
Sample mean =
= 2.36
Standard deviation = s = 1.19
We have to construct 95% confidence interval.
Formula is
Here E is a margin of error.
Degrees of freedom = n - 1 = 282 - 1 = 281
Level of significance = 0.05
tc = 1.968 ( Using t table)
So confidence interval is ( 2.36 - 0.1395 , 2.36 + 0.1395) = > ( 2.2205 , 2.4995)
-------------------------------------------------------------------------------------------------------------------
c) Sample size = n = 282
Sample mean =
= 2.36
Standard deviation = s = 1.19
We have to construct 99% confidence interval.
Formula is
Here E is a margin of error.
Degrees of freedom = n - 1 = 282 - 1 = 281
Level of significance = 0.01
tc = 2.593 ( Using t table)
So confidence interval is ( 2.36 - 0.1838 , 2.36 + 0.1838) = > ( 2.1762 , 2.5438)
-------------------------------------------------------------------------------------------------------------------
If the confidence level increase then the width of confidence interval also increases.
orchestra answered 1 year agoRelated Solutions
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